Question

write the equation for an exponential function, in the forms y = a x b^x, whose graph passes through the coordinate points (1, 7.5) and (3, 16.875).

Answer 1

y = abˣ
(a ≠ 0, b ≠ 0)

(1, 7.5)
x = 1
y = 7.5
    ↓
7.5 = ab

(3, 16.875)
x = 3
y = 16.875
        ↓
16.875 = ab³

   7.5 = ab
     b      b
7.5/b = a

    16.875 = ab³
         b³        b³
16.875/b³ = a

     7.5/b  = 16.875/b³
7.5/b(b³) = 16.875/b³(b³)
     7.5b² = 16.875
      7.5         7.5
          b² = 2.25
      √(b²) = √(2.25)
           b = 1.5

a = 7.5/b
a = 7.5/1.5
a = 5

y = 5(1.5)ˣ

Answer 2

Answer:

The the required exponential function is $y=5(1.5)^x$.

Step-by-step explanation:

The equation for an exponential function, in the forms

$y=ab^x$

It is given that passes through the coordinate points (1, 7.5) and (3, 16.875). It means the given function must be satisfied by these points.

$7.5=ab^1$

$7.5=ab$                        ....(1)

$16.875=ab^3$              ..... (2)

Divide equation (2) by equation (1).

$\frac{16.875}{7.5}={ab^3}{ab}$

$2.25=b^2$

$b=1.5$

The value of b is 1.5. Substitute b=1.5 in equation (1).

$7.5=a(1.5)$

Divide both sides by 1.5.

$a=5$

Therefore the required exponential function is $y=5(1.5)^x$.